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Compound interest earns returns on accumulated gains

Simple interest uses only the original principal. Compounding adds each period's gain to the balance used for the next period. With the same starting amount and positive rate, the difference becomes larger over time.

Start with 100 at an assumed 8% annual return. After one year, the balance is 108. Simple interest adds another 8 in year two, giving 116. Compounding instead adds 8% of 108, or 8.64, giving 116.64. The extra 0.64 is the return earned on the first year's gain.

Reinvesting dividends or interest can expand the base for future returns. If your assumed total return already includes dividends and price changes, do not add the dividend yield again. Withdrawing distributions produces a different outcome from this full-reinvestment assumption.

The formula and how to read the result

This calculator applies the annual return once per year to one initial investment. It assumes no later deposits or withdrawals and full reinvestment of each year's gains.

Final value = initial investment × (1 + annual return ÷ 100)^years

Initial investment

₩10,000,000

Estimated value after 10 years

₩21,589,250

Estimated growth

₩11,589,250

At 8%, the growth factor is 1.08. Over ten years, the initial amount is multiplied by 1.08 ten times. The simple-versus-compound example above uses these assumptions to show how reinvestment changes the ending balance.

Estimated value includes both principal and gains. Estimated growth is the ending value minus principal. Cumulative return divides that growth by the initial amount and describes the entire period, not a single year. Dividing a ten-year cumulative return by ten does not give its compound annual rate.

Time and the rule of 72: estimating when money doubles

At a constant positive rate, the annual percentage stays the same while the amount earned increases. Earlier gains become a larger part of the balance generating new gains. This explains the larger increases in the later intervals of the investment-period comparison above.

A quick doubling-time estimate is 72 divided by the annual return expressed as a percentage. An 8% rate suggests about nine years; a 6% rate suggests about twelve. This rule of thumb is approximate, so use the calculator to check actual projected values.

The estimate assumes a constant positive rate and no additional contributions. If you add savings every month, reaching twice your initial balance also reflects new deposits. That increase should be distinguished from investment growth alone.

Annual and monthly compounding depend on the rate definition

Annual compounding updates the interest base once a year; monthly compounding updates it once a month. For the same positive nominal annual rate, with a monthly rate of one twelfth of that rate, monthly compounding gives a larger final value because interest begins earning interest sooner.

Under that convention, the monthly formula is “initial investment × (1 + annual rate ÷ 100 ÷ 12)^{12 × years}”. If the input is an effective annual return that already includes compounding, the equivalent monthly rate is instead “(1 + annual return ÷ 100)^1/12 − 1”. This preserves the same annual growth.

This page uses annual compounding. Check a product's interest terms in the deposit interest calculator or recurring savings calculator. Stocks do not pay a fixed monthly interest rate, and changing the compounding interval cannot reproduce actual market movements.

Taxes, fees and inflation change what you keep

The projected balance is a nominal amount before taxes and fees. Recurring costs reduce the amount left to earn future returns. Tax treatment depends on the account, investment and timing, so applying one tax rate to every year's gain cannot reproduce every investor's take-home result.

Try a lower return assumption while keeping the starting amount and period unchanged. This helps show how lower performance or costs might affect a long-term plan. It does not automatically calculate product-specific fees or taxes.

Inflation reduces what a future amount can buy. For retirement or living-expense planning, use the inflation and purchasing power calculator to estimate the balance's purchasing power in today's money. Currency selection changes the input and display units; it does not convert amounts using exchange rates. Foreign-exchange movements are also excluded.

Monthly investing makes contribution timing matter

An initial lump sum grows for the full period, while later deposits grow only for the remaining time. Treating the sum of all monthly contributions as money invested on day one overstates projected growth. Equal total contributions can therefore produce different ending balances when deposited at different times.

The recurring investment calculator separates your initial amount from contributions made at each month-end. Compare a monthly saving plan there, or use the target asset calculator to estimate the monthly amount needed for a chosen final balance.

Compare different periods and return assumptions instead of treating one rate as a certain future. Actual investments can have losing years. A 20% gain followed by a 20% loss leaves 96% of the original amount, even though the arithmetic average of those two returns is zero.

Frequently asked questions